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Dynamically Consistent Conditional Choquet Capacities

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Author Info
Robert Kast ()
André Lapied

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Abstract

Preferences of a Decision Maker define a valuation function on future uncertain payoffs. Consistency of this unconditional valuation function with valuation conditional on information arrivals is justified by a no Money Pump argument. A result on the updating of capacities is obtained in a static framework. Then the arguments are developed in a model where the future payoffs are contingents on two components: uncertain states and future dates. We obtain results on updating capacities on the uncertain states and “upstating” capacities (discount factors) on future dates in a special case. These results are shown to violate consequentialism.

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Publisher Info
Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 20-2007.

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Length: 34 pages
Date of creation: Mar 2007
Date of revision:
Handle: RePEc:icr:wpmath:20-2007

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Related research
Keywords: Comonotonicity; Capacities on product spaces; Updating; Flexibilities;

Find related papers by JEL classification:
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
D92 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Firm Choice and Growth, Investment, or Financing
G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Investment Policy

References listed on IDEAS
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  1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February. [Downloadable!] (restricted)
    Other versions:
  2. Kreps, David M & Porteus, Evan L, 1979. "Dynamic Choice Theory and Dynamic Programming," Econometrica, Econometric Society, vol. 47(1), pages 91-100, January. [Downloadable!] (restricted)
  3. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January. [Downloadable!] (restricted)
  4. Kiyohiko G. Nishimura & Hiroyuki Ozaki, 2003. "A Simple Axiomatization of Iterated Choquet Objectives," CIRJE F-Series CIRJE-F-219, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  6. Karni, Edi & Schmeidler, David, 1991. "Atemporal dynamic consistency and expected utility theory," Journal of Economic Theory, Elsevier, vol. 54(2), pages 401-408, August. [Downloadable!] (restricted)
    Other versions:
  7. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November. [Downloadable!] (restricted)
  8. Diecidue, Enrico & Wakker, Peter P., 2002. "Dutch books: avoiding strategic and dynamic complications, and a comonotonic extension," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 135-149, March. [Downloadable!] (restricted)
  9. Ghirardato, Paolo, 1997. "On Independence for Non-Additive Measures, with a Fubini Theorem," Journal of Economic Theory, Elsevier, vol. 73(2), pages 261-291, April. [Downloadable!] (restricted)
    Other versions:
  10. De Waegenaere, Anja & Kast, Robert & Lapied, Andre, 2003. "Choquet pricing and equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 359-370, July. [Downloadable!] (restricted)
  11. Hammond, Peter J, 1989. "Consistent Plans, Consequentialism, and Expected Utility," Econometrica, Econometric Society, vol. 57(6), pages 1445-49, November. [Downloadable!] (restricted)
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